They do not have Computers. They do have electronics.
The condenser coil, the distributer, voltage regulator and the alternator are all vulnerable to an EMP.
Not to mention that the battery is likely to explode.
It is the sensitive gate channel of a mosfet that is vulnerable to the EMP blast. Not unlike an ESD hit. Probably other areas such as the substrate that interfere with the ICs function but it will continue to operate after the source is removed.
An EMP is simply a massive amount of fairly broad band noise that interferes with modern electronics.